What properties allow something to be considered "milk"?

Traditionally, milk is defined as (from Merriam-Webster):

1: a white liquid produced by a woman to feed her baby or by female animals to feed their young; especially : milk from cows or goats that is used as food by people

2: a white liquid produced by a plant

In today's day and age, if you go to a grocery store (or coffee shop) you can get many varieties of milk: animal milk, lactose-free animal milk, soy milk, coconut milk, rice milk, almond milk, hemp milk, and more.

My question is, is the traditional definition of milk complete? Are there any exceptions to definition #2 of milk (i.e. white liquids produced by plants that are NOT considered milk, or non-white liquids produced by plants that ARE considered milk)? What other properties do all milks share that allow them to be substitute ingredients in the same products?